Brother Can You Spare 18 Cents?

Americans have had it with loose change. It bursts pockets, fills piggy banks, spills from the little change bowl by the front door. By one estimate, $10.5 billion in coins just sits around in people’s homes gathering dust. What with fancy purses and expensive pocketbooks, “power wrappers,” and automated coin sifters, it’s fair to say that a decent chunk of that do-nothing change is spent simply trying to organize it.

Jeffrey Shallit has a suggestion. A mathematician at the University of Waterloo in Ontario, Shallit recently analyzed the average handful of change and has devised a clever way to reduce its size.

Getting rid of the 1-cent coin, a plot advocated by numerous antipennyists, would certainly help, he says. But Shallit’s own scheme for reducing loose change involves the creation of an entirely new coin. What the United States needs, he says, is an 18-cent piece.

Shallit reached this conclusion by way of a common mathematical formula called a linear Diophantine equation, which dates back some 1,750 years to Diophantus, the Greek father of algebra. The simplest form of the equation looks like something straight out of a high school textbook: ax + by + . . . = c.

Straightforward as they may appear, Diophantine equations…

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